Essentials of Computational Chemistry

11.4 STRENGTHS AND WEAKNESSES OF CONTINUUM SOLVATION MODELS 421
for modeling pathways associated with protein folding (see, for instance, Jang, Shin, and Pak
2002 and Chowdhury et al. 2003), the timescale for which would have made simulations
with explicit solvent prohibitively expensive. Of course, if one is interested in the kinetics
of the process in question, then removal of the solvent friction is not helpful – the implicit
solvent advantage applies only to obtaining rapid equilibrium averages.
As for the quality of the energy landscape and its effect on solute dynamics, comparisons
of PCA eigenvectors from simulations using either implicit or explicit solvation have been
carried out for proteins (Cornell et al. 2001), DNA (Tsui and Case 2000) and RNA (Sherer
and Cramer 2002) and have generally indicated high overlap between the two models. Nevertheless,
some protein folding studies have identified serious deficiencies in GB landscapes
that include overestimation of salt-bridge interaction energies (Zhou 2003) and a general
tendency to overstabilize nucleation (Nymeyer and Garcia 2003). One alternative to propagating
a trajectory using an implicit solvent model that has also been explored has been
to take a trajectory generated with inclusion of explicit solvent and then post-process it to
compute individual or average solvation free energies for various snapshots, whose computation
would otherwise require more sophisticated simulation protocols as described in the
next chapter.
Some work has also appeared describing MD with implicit solvation for solutes described
at the DFT level. Fattebert and Gygi (2002) have proposed making the external dielectric
constant a function of the electron density, thereby achieving a smooth transition from solute
to solvent instead of adopting a sudden change in dielectric constant at a particular cavity
surface. Non-electrostatic components of the solvation free energy have not been addressed
in this model.
11.4.6 Equilibrium vs. Non-equilibrium Solvation
Most continuum models are properly referred to as ‘equilibrium’ solvation models. This
appellation emphasizes that the design of the model is predicated on equilibrium properties
of the solvent, such as the bulk dielectric constant, for instance. The amount of time required
for a solvent to equilibrate to the sudden introduction of a solute (i.e., the solvent relaxation
time) varies from one solvent to another, but typically is in the range of molecular vibrational
and rotational timescales, which is to say on the order of picoseconds.
Processes that take place on longer timescales may thus be legitimately thought of as
equilibrium processes with respect to solvation. However, the question arises of how applicable
continuum models are to very fast processes. For instance, Figure 11.4 describes the
relationship between gas-phase and solvated reaction coordinates for a reactive process, but
the average amounts of time individual molecules spend at various positions on the reaction
coordinate vary considerably. In the regions of the minima, equilibrium solvation seems
assured, but transition state structures in principle live for only a single vibrational period.
This suggests that the solvent may not have time to fully equilibrate to the TS structure, and
a continuum model were it to be applied would overestimate the solvation free energy by
assuming equilibration. In addition, considerable progress has been made in the extension
of GB models to systems where an implicit membrane characterized by a dielectric constant